Logarithmic Gysin sequences for regular immersions

2024/04/05 by Park, Doosung
#14A21 #14F42 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.04082

Abstract

For a regular immersion of schemes Z→ X and a cohomology theory of fs log schemes, we formulate the logarithmic Gysin sequence using the "logarithmic compactification" (Bl_Z X,E) instead of the open complement X-Z, where E is the exceptional divisor. We show that all \mathbbA¹-invariant cohomology theories produced from motivic spectra and various non \mathbbA¹-invariant cohomology theories like Nygaard completed prismatic cohomology admit logarithmic Gysin sequences.

Related

• Construction of logarithmic cohomology theories I
• Logarithmic A_{\rm inf}-cohomology
• Logarithmic motives with compact support
• Logarithmic De Rham, Infinitesimal and Betti Cohomologies
• Logarithmic prismatic cohomology, motivic sheaves, and comparison theorems